Functional Analysis

Code: MA731 | L-T-P-C: 4-0-0-8

MA731 Functional Analysis L-T-P-C [4-0-0-8]

Prerequisites: Nil

Review of normed spaces and Banach spaces; Bounded linear operators, Hahn-Banach theorem, Dual spaces, Open mapping theorem, Closed graph theorem, Uniform boundedness principle; Weak and weak* topologies, Alaoglu theorem; Compact operators, Riesz theory for compact operators; Spectra of bounded linear operators, Gelfand-Mazur Theorem.

Review of inner product spaces and Hilbert spaces; Orthonormal bases, Riesz representation theorem; Adjoint of a bounded linear operator, Self-adjoint, normal and unitary operators; Spectral theorem of compact self-adjoint/normal operators.

Texts/References:

1. R. Bhatia: Notes on Functional Analysis (Hindustan Book Agency)
2. J. B. Conway: A Course in Functional Analysis, 2nd edition (Springer low price edition)
3. B. V. Limaye: Functional Analysis, 3rd edition (New Age Publishers)
4. M. Schechter: Principles of Functional Analysis, 2nd edition (Universities Press)